Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

An occupational view of the Australian labour force - Patterns of job growth and decline

Generally employment has been studied in terms of changes in the types of goods and services that the economy is purchasing. Far less attention has been given to the occupational aggregates that go into producing these goods and services. The few studies that did investigate this area found that the mix of tabour inputs appear to have been changing over time in a systematic pattern. The increasing prevalence of white-collar, information workers gave rise to the assertion that many societies had entered a post-industrial information age. Deals first of aff with some issues of measurement in the context of the Australian labour force, then looks at trends in various occupational groups using a non-standard four-sector classification of the labour force. Finally suggests an application in relation to the link between education and training and its ability to reduce structural unemployment.

Factors influencing job valuation: a comparative study of critical care and mon-critical care nurses

This study sought to identify the relationship between three predictor variables. perceived collaboration with medical staff, autonomy and independent actions and an outcome. the value hospital nurses placed on their work. In total 189 critical care and 366 non-critical care nurses completed a mailed survey. Critical cure nurses perceived themselves to have a mure collaborative relationship with the medical staff. described performing actions independent of medical orders more frequently and perceived their jobs to have more value than non-critical care nurses. However the latter group perceived themselves to have more autonomy in their work. Within both groups collaboration and autonomy were significantly, but weak to moderately correlated with job valuation. Simply expanding the work hospital nurses do is unlikely to result in nurses valuing their jobs more. however promoting an environment of respect and sharing between the medical and nursing staff and supporting nurses when they act in an autonomous fashion may positively influence nurses' perceptions of their work. (C) 2001 Elsevier Science Ltd. All rights reserved.

Autonomy: an important component for nurses' job satisfaction

This quantitative pilot study (n = 178), conducted in a large Brisbane teaching hospital in Australia, found autonomy to be the most important job component for registered nurses' job satisfaction. The actual level of satisfaction with autonomy was 4.6, on a scale of 1 for very dissatisfied to 7 for very satisfied. The mean for job satisfaction was 4.3, with the job components professional status and interaction adding most substantially to the result. There was discontentment with the other two job components, which were Cask requirements and organisational policies. Demographic comparisons showed that nurses who were preceptors had significantly less job satisfaction than the other nurses at the hospital. (C) 2001 Elsevier Science Ltd. All rights reserved.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.